score:27
It seems like this was the 'polite' gesture of greeting in ancient Sumeria, and is actually the meaning of a Sumerian phrase for greeting:
She faces in the direction of the cultic activity, her right arm bent at the elbow, hand raised before the face, in a well-known gesture of pious greeting, comparable to those depicted in presentation scenes, from Ur III seals to the Code of Hammurabi, and finding its literary referent in the Sumerian verb “to greet”—kiri šu-gal—literally, “to let the hand be at the nose.”
The above from On Art in the Ancient Near East Volume II: From the Third Millennium BCE By Irene Winter (emphasis mine)
I'm not sure, but this image may represent the above described gesture:
From Code of Hammurabi
Another cylinder seal, this one linked to Ur-Nammu, (probably a little earlier then your preferred time), seems to show the same gesture:
Concerning comments questioning the exact position of the hand (and the number of hands used), another reference, Babylonian Poems of Pious Sufferers: Ludlul Bel Nemeqi and the Babylonian Theodicy by Takayoshi Oshima, suggests there is still some ambiguity concerning this:
Kiri Suga, literally 'to place the hand(s) (on) the nose', it is evident that the gesture involves both nose and hand, yet their exact positions have not yet been established.